The topics covered in this course are fundamental for graduate students in the area of electromagnetics. This course builds upon undergraduate electromagnetic courses and enables the students to gain an in-depth understanding of fundamental electromagnetic concepts, theorems, and analytical techniques. The course also provides an introduction of numerical techniques that are becoming increasingly important in solving electromagnetic wave problems in complex geometries. Many topics covered in this course are essential for graduate courses in areas such as radio frequency and microwave engineering, antennas, photonics, and space sciences.